This paper develops a theory of inflation inertia based on forward looking staggered price setting in the nontradable goods sector of a small open economy. Unlike current theories of sticky prices, transitions to a lower steady state inflation rate take time even if they are fully credible, and they are associated with significant output losses in nontradables There is a welfare trade-off between these output losses and the gains from smaller inflationary distortions. Gains exceed losses for most calibrations. The optimal steady state is the Friedman rule.